Here's one possibility.....it's known as the greatest  interger function :

https://www.wolframalpha.com/input/?i=greatest+integer+function

It's denoted   as    shown here   : 

http://www.mathwords.com/c/ceiling_function.htm

Note

lim  f(x)     =    1        

x → 2^- 

But

lim  f(x)     =    2        

x → 2⁺

128 lbs is about 58 kg.  Assuming the 5mm refers to the diameter of the stilleto heel, then:

force = 58*9.8 N → 568.4 N

area = pi*0.0025^2 m^2 ≈ 2*10^-5 m^2

pressure = force/area → 568.4/(2*10^-5) N/m^2 ≈ 284^10^5 N/m^2 or 284 bar.

This assumes the wearer is standing on one heel!  If standing on two heels the pressure will be halved. if standing on more of her feet than just heels the pressure will be reduced further.

.

.

sec (10°)  =  csc (90 - 10)°  =  csc (80°)

sec (10° )   ≈  1.0154

\(\text{In contrast to what has been said before the union of two linear subspaces of }V\\ \text{ is in general not a linear subspace itself. Take for example the linear vector space}\\ \mathbb{R}^2\text{ of two dimensional vectors. We can now define the two following subspaces:}\\ M=\{(a,0);a\in\mathbb{R}\},\\ N=\{(0,b);b\in\mathbb{R}\}.\\ \text{It should be clear that each individual subspace is a linear subspace of }\mathbb{R}^2. \text{The}\\ \text{union of the two is not a linear subspace because the vector (1,1) is not an element}\\ \text{of the union (which it should be since (1,0) and (0,1) are elements of the union).}\\ \text{Hence the given statement is disproven by means of counterexample.}\)

I do not understand what you mean Max :/

Here is a pretty tesselation, what angles are you referring to?

If any combination of its interior angle can add up to 360 deg, then it can tesselate :)

I am not sure about this, but if this is wrong, this is close already.(I think...)

Someone please help modify my statement.

Of course Max is correct, there has to be an angle there. :)

or

(tan30)^2 = 1/3

The calc changes it to tan30^2 but that is ok :)

(tan(30))^2 = 0.3333333333337655

It should just be 1/3 so there is some rounding error.

Tangent is a function, and tan² have no value. 

OK I understand a bit now :) Thanks

I don't have a general answer for you, but that is a good question ://

\(\int_{0}^{5} h(x)dx = 0\)

That is what I got after trying to figure out the area of a square using an integral. h(x) = 5 creating a square... the area is 25 but why this integral no work? A line is a curve too!!!

h(x)=5

\(A=\int_{0}^{5} h(x)dx \\ =\int_{0}^{5} \;5\:dx \\ =\left[5x\right]_0^5\\ =25-0\\ =25 units^2 \)

My integral works just fine.   

Thanks Heureka,

But the curved graph does not go through those 2 points.

Here is a bigger version of the graph.

I think it goes through the points (2.75,2.75) (1.75,5) and (5,1.75)

How do I find a graph that will go through these points ?? 

First, the integral of 5 with respect to x is 5x

Next, you evaluate this 5x at x=5 and at x=0

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Your solution to answer is great . However i have other solution to this problem : 

10+1^0 =11 , 11+1^1=12 , 12 +1^2 =13 , 13+1^3=14 .... we also have 20+2^0=21 ,21+2^1=23, 23+2^3=31 

So my answer is 23 . Hope to see your response soon ! Thanks

To find half of 34  »»»  

 2   1/x   x  34   =

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The union of two subspaces just means that we include all of the elements of each subspace into another space,obeying the same rules as they did before.Here the elements are vectors.( This just like the union of two sets.no different.)

So you have all the vectors in subspace M and all the vectors in subspace N together. Since you are told that the vector  x is either in M or N,then the union of M and N must contain ALL the vectors  x ,and they must be linearly independent.(Since they are linearly independent in both M  AND in N)

Now ,both linear subspaces obey a(x1 + x2)  = ax1  + ax2   where x1,x2  are any two linearly independent  vectors in either M or N. 

 Finally,if x is in either M or N,it cannot be outside M or N,so you cannot find vectors x, outside M U N,hence  M U N must be a linear subspace of V.        (take heart,no-one finds this stuff easy to begin with.)

To find tan² you first find tan, then you square that.  

tan² 30° = (tan 30°)x(tan 30°)

Its either in N, in M or in both of them

Hmm? I don't quite understand...

So the union of M and N means it is either in M or in N?

how to calculate 14^15 mod 15

that's hard!! 

*VERY* Hard Math Question for my profile picture

I assume two points of the hyperbola are: \(P_1(4,2) \text{ and } P_2 (2,4)\)

Then the hyperbola equation is \( xy = 8\), because the Area under the hyperbola is 4*2 = 2*4 = 8 and \(y_{\text{hyperbola}} = \frac{A}{x}\)

The other equation is a line \( y = x\)

The intersect Point:

\(\begin{array}{|rcll|} \hline xy&=&8 \quad & | \quad y=x \\ x\cdot x &=&8 \\ x^2 &=&8 \\ x^2 &=&2\cdot 4 \\ x_{\text{intersection} } &=& 2\sqrt{2} \\\\ y_{\text{intersection} } &=& x_{\text{intersection} } \\ y_{\text{intersection} } &=& 2 \sqrt{2} \\ \hline \end{array}\)

The intersect Point is: \((2\sqrt{2},\ 2 \sqrt{2} )\)

The picture is:

14^15 mod 15

\(\begin{array}{|rcll|} \hline \mathbf{ 14^{15} \pmod {15} =\ ? } \\\\ && 14^{15} \pmod {15} \quad &| \quad 14 \equiv -1 \pmod {15} \\ &\equiv& (-1)^{15} \pmod {15} \quad &| \quad (-1)^{15} = -1 \\ &\equiv& -1 \pmod {15} \\ &\equiv& -1 +15 \pmod {15} \\ &\equiv& 14 \pmod {15} \\\\ \mathbf{ 14^{15} \pmod {15} = 14 } \\ \hline \end{array} \)